Institut de Mathématiques de Marseille, UMR 7373




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Séminaire Dynamique, Arithmétique, Combinatoire (Ernest)

par Drappeau Sary, Guillon Pierre, Lozingot Eric, Merlet Glenn - publié le , mis à jour le

Agenda

Séminaire

  • Mardi 12 décembre 11:00-12:00 - Sergiy Kolyada - Institute of Mathematics, NAS of Ukraine/IHES

    Dynamical Topology : Slovak Spaces and Dynamical Compactness

    Résumé : The area of dynamical systems where one investigates dynamical properties that can be described in topological terms is called "Topological Dynamics". Investigating the topological properties of spaces and maps that can be described in dynamical terms is in a sense the opposite idea. This area is called "Dynamical Topology".
    For (discrete) dynamical systems given by compact metric spaces and continuous (surjective) self-maps, I will mostly be talking about two new notions : "Slovak Space" and "Dynamical Compactness". Slovak Space is a dynamical analogue of the rigid space : a nontrivial compact metric space whose homeomorphism group is cyclic and generated by a minimal homeomorphism.
    Dynamical Compactness is a new concept of chaotic dynamics. The ω-limit set of a point is a basic notion in theory of dynamical systems and means the collection of states which "attract" this point while going forward in time. It is always nonempty when the phase space is compact. By changing the time we introduced the notion of the ω-limit set of a point with respect to a Furstenberg family. A dynamical system is called dynamically compact (with respect to a Furstenberg family) if for any point of the phase space this ω-limit set is nonempty. A nice property of dynamical compactness :
    all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property.
    Based on a work by Tomasz Downarowicz, Lubomir Snoha and Dariusz Tywoniuk, and joint works with Wen Huang, Danylo Khilko, Alfred Peris, Julia Semikina and Guohua Zhang.
    http://www.imath.kiev.ua/ skolyada/

    Lieu : 306, Luminy

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  • Mardi 19 décembre 11:00-12:00 - Benoît Saussol - Laboratoire de Mathématiques de Bretagne Atlantique

    Linear response for random dynamical systems

    Résumé : We study for the first time linear response for random compositions of maps, chosen independently according to a distribution ℙ. We are interested in the following question : how does an absolutely continuous stationary measure (acsm) of a random system change when ℙ changes smoothly to ℙε ? For a wide class of one dimensional random maps, we prove differentiability of acsm with respect to ε ; moreover, we obtain a linear response formula. We apply our results to iid compositions of uniformly expanding circle maps, to iid compositions of the Gauss-R\’enyi maps (random continued fractions) and to iid compositions of Pomeau-Manneville maps.
    https://arxiv.org/abs/1710.03706

    Lieu : 306, Luminy

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  • Mardi 16 janvier 2018 11:00-12:00 - Anna Frid - I2M

    Systèmes sturmiens de numération et palindromes

    Résumé : Je généralise les systèmes de numération d’Ostrowski pour décrire les occurrences des palindromes à un mot sturmien caractéristique et démontrer une conjecture sur les décompositions des facteurs sturmiens en produit de palindromes.

    Lieu : 306, Luminy

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groupe de travail

Manifestation scientifique

Descriptif
Nature Séminaire
Intitulé Dynamique, Arithmétique, Combinatoire (Ernest)
Responsables Sary Drappeau & Pierre Guillon
Équipe de rattachement Géométrie, Dynamique, Arithmétique, Combinatoire
et leurs interactions (GDAC)
Fréquence Hebdomadaire
Jour-Horaire Mardi. 
11h05-12h
Lieu Luminy, salle des séminaires 304-306 (accès)
Lien -